Irish songs? The ears perk up...
Of course, it depends on where you're singing. I never had much luck singing at instrumental sessions -- they never knew what to do with a vocalist, especially if she wasn't someone's girlfriend.
If you think people are really going to stop playing and listen, try "If I Was a Blackbird" or "Galway Shawl". "Fanny Power" (aside from being a terrific feminist slogan!) is a nice tune, and there are decent English lyrics recorded by the trio Cailleach.